With computational demands in genetics growing exponentially, concerns are rising whether traditional CPUs can deliver the needed computing power. Parallel computing has been touted for several years, but massively parallel CPU computers are enormously expensive and limited to a few national centers. Graphics processing units (GPUs) offer a far cheaper and more distributed solution. Hundreds of these units are fabricated on a single card, and several cards fit inside a desktop computer. Thus, cheap hardware currently exists that promises a hundred-fold speedup of many basic algorithms. Projections from the vendors of GPUs suggest that these devices will grow rapidly in computational power and versatility over the next decade. Thus, software development is the main hurdle hindering the exploitation of GPUs. This proposal targets this weak link in the chain of modern computing. Through a series of demonstration projects and the production of low-level software libraries, we hope to catalyze the spread of GPUs in genetics. The specific projects include: 1) eQTL mapping, 2) variance component models for QTL mapping, 3) genotype and haplotype construction, 4) estimation of ethnic admixture, 5) isoform discovery through RNA-Seq technology, 6) computation of genetic landscapes and clines, 7) construction of gene networks from random multigraphs, and 8) design of new parallel algorithms for data mining. High-dimensional optimization is a common thread enabling all of these applications. Our previous research on optimization has demonstrated the efficacy of four fundamental ideas, namely, penalized estimation, coordinate descent, the MM (majorization-minimization) principle, and separation of parameters. These ideas also propel parallel computing. Implementation of our demonstration projects on GPUs will require the production of subroutines of considerable general value in computational statistics. We intend to release our toolbox libraries to the open source community, including C/C++, Fortran, and R software wrappers. This may lead to a multiplier effect that will improve the computing climate in many disciplines throughout the health and physical sciences. All other application programs produced under this proposal will be freely distributed to the scientific community. Our record of producing and distributing usable software with superior documentation shows our commitment to this philosophy.